|
| |
|
|
A123853
|
|
Numerators in asymptotic expansion of cubic recurrence sequence A123851.
|
|
5
| |
|
|
1, 3, -15, 113, -5397, 84813, -3267755, 74391561, -15633072909, 465681118929, -31041303829713, 1145088996404679, -185348722911971841, 8165727090278785521, -778296382754673737187, 39898888480559205453945, -35033447016186321707305533
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| A cubic analog of the asymptotic expansion A116603 of Somos's quadratic recurrence sequence A052129. Denominators are A123854.
|
|
|
REFERENCES
| S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. 332 (2007) 292-314.
|
|
|
LINKS
| J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant
Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant
|
|
|
EXAMPLE
| A123851(n) ~ c^(3^n)*n^(- 1/2)/(1 + 3/4n - 15/32n^2 + 113/128n^3 - 5397/2048n^4 + ...) where c = 1.1563626843322... is the cubic recurrence constant A123852.
|
|
|
MAPLE
| f:=proc(t, x) exp(sum(ln(1+m*x)/t^m, m=1..infinity)); end; for j from 0 to 29 do numer(coeff(series(f(3, x), x=0, 30), x, j)); od;
|
|
|
PROG
| (PARI) {a(n) = local(A); if(n < 0, 0, A = 1 + O(x) ; for( k = 1, n, A = truncate(A) + x * O(x^k); A += x^k * polcoeff( 3/4 * (subst(1/A, x, x^2/(1-x^2))^2/(1-x^2) - 1/subst(A, x, x^2)^(2/3)), 2*k ) ); numerator( polcoeff( A, n ) ) ) } /* Michael Somos Aug 23 2007 */
|
|
|
CROSSREFS
| Cf. A052129, A112302, A116603, A123851, A123852, A123854.
Sequence in context: A058104 A056053 A059849 * A166885 A082163 A190629
Adjacent sequences: A123850 A123851 A123852 * A123854 A123855 A123856
|
|
|
KEYWORD
| frac,sign
|
|
|
AUTHOR
| Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006
|
| |
|
|
